δ-SUPERDERIVATIONS OF SIMPLE FINITE-DIMENSIONAL JORDAN AND LIE SUPERALGEBRAS

We introduce the concept of a delta-superderivation of a superalgebra. delta-Derivations of Cartan-type Lie superalgebras are treated, as well as delta-superderivations of simple finite-dimensional Lie superalgebras and Jordan superalgebras over an algebraically closed field of characteristic 0. We give a complete description of 1/2-derivations for Cartan-type Lie superalgebras. It is proved that nontrivial delta-(super) derivations are missing on the given classes of superalgebras, and as a consequence, delta-superderivations are shown to be trivial on simple finite-dimensional noncommutative Jordan superalgebras of degree at least 2 over an algebraically closed field of characteristic 0. Also we consider d- derivations of unital flexible and semisimple finite-dimensional Jordan algebras over a field of characteristic not 2.